Sounds like you may need to adjust the top tension. Sew on a couple long scrap pieces until this doesn't happen any more.

You didn't mention whether or not you prewashed your fabric or not. I would try that and then press with starch or starch alternative.

This very thing happened to me about a month ago...I ended up having to do both, adjust my tension and lengthen my stitch. Hope you have been successful in solving your problem.

I recently learned to use the Creative Grids Curvy Log Cabin tool to make log cabin blocks and the instructor told us: when adding another log, sew with the already pieced side UP. In other words, when adding a piece to other pieces that are already sewn, put the new piece on the bottom, and the previously stitched piece on top. This worked great for me and my log cabin blocks came out great. Maybe you could try this method and see what happens.
Hope I am understanding what you are stating is the problem.

Wow - lots of good advice. This is a Pfaff 4.2 which I have had for about 10 months. I did not know you can adjust the height of the feed dogs. I will look into that and try all the suggestions you have mentioned. I have a big testing day ahead of me. Thanks everyone for taking the time to help me.

Just recently, I think it was yesterday, Donna showed how she put her fingers on the pieces as they were supposed to go through the needle and held them there as the piece went up to the needle.

A few months ago I saw someone else do what I always do. I hold onto the seam after I have it aligned the way I want it, a few inches from the needle. As it is going into the needle, with the other hand, hold the seam as it comes out from behind the needle. I actually pull on this seam as I let it go through as fast as the feed dogs want it to.

You wouldn't want to do this with bias seams, but bias seams are easier to line up anyway. Just keep the beginning and end in the right place and keep it flat as it goes through the needle.

That happens to me if I should pull on the fabric rather then letting it glide through the feed dogs. Hope that makes sense.

I had the same problem. I solved mine by using a 'leader' and not starting on the main fabric.

I use a leader and place a piece of scotch tape over the seam in the metal just before the needle plate, that seems to help a lot, also keeps those seams from turning over on the backside.

I wonder if when you sew the first two pieces together you don't maintain the full 1/4 all the way off the end; I sometimes have trouble with the fabric veering off and get less than a 1/4" seam allowance. Then when you sew the next piece on it would show a slight pleat or pucker at that point. Might try using a stilletto to keep the fabric at 1/4 seam.